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Stratified Sampling of Spherical Triangles Program of Computer Graphics \Lambda

Summary: Stratified Sampling of Spherical Triangles
James Arvo
Program of Computer Graphics \Lambda
Cornell University
We present an algorithm for generating uniformly dis­
tributed random samples from arbitrary spherical triangles.
The algorithm is based on a transformation of the unit
square and easily accommodates stratified sampling, an ef­
fective means of reducing variance. With the new algorithm
it is straightforward to perform stratified sampling of the
solid angle subtended by an arbitrary polygon; this is a fun­
damental operation in image synthesis which has not been
addressed in the Monte Carlo literature. We derive the re­
quired transformation using elementary spherical trigonom­
etry and provide the complete sampling algorithm.
CR Categories and Subject Descriptors: I.3.5 [Com­
putational Geometry and Object Modeling]: Geometric Al­
Additional Key Words and Phrases: Monte Carlo, solid


Source: Arvo, Jim - Departments of Information and Computer Science & Electrical and Computer Engineering, University of California, Irvine


Collections: Computer Technologies and Information Sciences